ForumSpringerAstron. Astrophys.
ForumWhats NewSearchOrders

Astron. Astrophys. 317, 73-81 (1997)

Table of Contents
Available formats: HTML | PDF (508 KB) | (gzipped) PostScript (1246 KB)

A fast method for distinguishing between ordered
and chaotic orbits

G. Contopoulos and N. Voglis

Department of Astronomy, University of Athens Panepistimiopolis, GR-15784 Athens, Greece

Received 14 February 1996 / Accepted 17 May 1996


We describe a new method of distinguishing between ordered and chaotic orbits, which is much faster than the methods used up to now, namely (1) the distribution of the Poincaré consequents, (2) the Lyapunov characteristic number and (3) the distribution of the rotation angles. This method is based on the distribution of the helicity angles (the angles of small deviations [FORMULA] from a given orbit with a fixed direction), or of the twist angles (the differences of successive helicity angles), and the stretching numbers (the logarithms of the ratios of successive deviations [FORMULA], also called 'short time Lyapunov characteristic numbers'). We apply this method to 2-D mappings and 4-D mappings, representing Hamiltonian systems of 2 and 3 degrees of freedom respectively.

Key words: chaos — stellar dynamics — Galaxy: kinematics and dynamics

Send offprint requests to: G. Contopoulos

© European Southern Observatory (ESO) 1997